Partial Differential Equations and Boundary-Value Problems with Applications
Seiten
2011
|
Third Edition
American Mathematical Society (Verlag)
9780821868898 (ISBN)
American Mathematical Society (Verlag)
9780821868898 (ISBN)
Building on the basic techniques of separation of variables and Fourier series, this presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems – rectangular, cylindrical, and spherical.
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Mark A. Pinsky, Northwestern University, Evanston, IL, USA
Preface
Chapter 0. Preliminaries
Chapter 1. Fourier Series
Chapter 2. Boundary-Value Problems in Rectangular Coordinates
Chapter 3. Boundary-Value Problems in Cylindrical Coordinates
Chapter 4. Boundary-Value Problems in Spherical Coordinates
Chapter 5. Fourier Transforms and Applications
Chapter 6. Asymptotic Analysis
Chapter 7. Numerical Analysis
Chapter 8. Green's Functions
Appendixes
Answers to Selected Exercises
Index
About the Author
| Erscheint lt. Verlag | 1.10.2011 |
|---|---|
| Reihe/Serie | Pure and Applied Undergraduate Texts |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 1120 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-13 | 9780821868898 / 9780821868898 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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